“It is the Academy's wish that I leave my post as permanent secretary,” Danius said after an emergency meeting of academy members in Stockholm.
“I would have liked to have continued, but there are other things to do in life,” she told reporters.
Also stepping down is Academy member Katarina Frostenson, a Swedish writer and the wife of the man at the centre of the scandal, Jean-Claude Arnault, a high-profile figure on Sweden's cultural scene.
The resignations come after the daily Dagens Nyheter in November published statements from 18 women, alleging they had been subject to harassment and physical abuse by Arnault.
He denies the accusations and police investigations into the allegations have been dropped.
He has also been accused of leaking the names of several Nobel Prize winners before the official announcements. Concerns have also been raised of a conflict of interest after it emerged that his wife is a part-owner of his culture venue, which has received financial support from the academy.
The academy has since severed all ties with him and cut grants made to him.
It also launched an internal investigation and enlisted the services of a law firm, which recommended that the academy file a police report. However, it did not take such action.
The academy, which is under the direct patronage of the Swedish king, is traditionally very discreet and has been deeply shaken by the scandal.
The head of the Nobel Foundation, Lars Heikensten, has publicly expressed concern about what he termed a “serious and difficult situation”.
Three academics resigned last week in protest after the institution had expressed renewed confidence in Frostenson, who finally announced her resignation on Thursday.
According to Peter Englund, one of the three who resigned, the case has deeply divided the institution.
He believes that Sara Danius, who succeeded him in 2015, is the target of “unwarranted” internal criticism.
Another member , Horace Engdahl, said that there was “a problem of leadership”.
“A radical gesture was needed to create the conditions for a new beginning,” he told Swedish public television SVT.
A professor of literature at Stockholm University, Danius was the first woman to hold the position.
She had been credited with trying to open up the closed institution to the public and bring it into the modern era, but her style of leadership has proved divisive.
Most of the Swedish culture and literature world appeared to come out in defence of Danius on Friday. Many people, including former academy head Englund, vowed to wear a pussy cat bow blouse, Danius' signature fashion choice. The Swedish word for such a blouse #knytblus was trending on Twitter on Friday morning.